Tidal locking as a negative feedback on Earth-like planetary dynamos: Consequences for magnetic shielding and habitability

We investigate how tidal locking affects the magnetic field generation and magnetospheric protection of Earth-like planets orbiting the habitable zone of M dwarfs. While the role of stellar activity has been widely studied, the impact of tidal locking on the planetary dynamo remains largely unexplored. We develop a framework that couples the stellar wind with two distinct dynamo paradigms: direct rotational scaling of a dipolar field, and energy-flux scaling where the local Rossby number governs the magnetic geometry, capturing a rapid transition from a dipolar to a multipolar configuration. We employ a Constant Time Lag model to capture the continuous tidal spin-down of the planets, evaluating two distinct planetary interiors: a highly dissipative Modern Earth and a less dissipative, rapidly rotating Early Earth. We find that tidal locking acts as a severe negative feedback on planetary magnetism across both paradigms, where the dipolar field frequently collapses before full tidal synchronization is reached. At the inner boundary, nearly all the planets are rapidly locked and the intrinsic magnetic fields are significantly attenuated. The outer boundary provides a favorable environment only for early M dwarfs (M 0.32 M) hosting Early Earth. Here, the combination of non-synchronous rotation and residence outside the sub-Alfv'enic regime provides atmospheric protection likelihoods of 97-100%. For mid-to-late M dwarfs, the combination of inevitable tidal locking and a sub-Alfv'enic environment results in a total collapse of the magnetic shield, reducing the likelihood of atmospheric protection to essentially zero across the entire habitable zone.